[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123445-en":3,"doc-seo-123445-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123445,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","E(2)-Equivariant Features in Machine Learning for Morphological Classification of Radio Galaxies","With the expansion of data from modern radio telescopes, machine learning is increasingly used to classify radio galaxy morphologies. Many deep models such as convolutional neural networks are translation-equivariant, yet they are not equivariant to other Euclidean-plane isometries like rotations and reflections. Instead of using E(2)-equivariant steerable CNNs, this work evaluates directly extracted E(2)-equivariant features—Minkowski functionals, Haralick features, and elliptical Fourier descriptors—for classification. The study shows far lower computational cost (~50× runtime reduction) with informative, though less accurate, feature sets and highlights overlap effects when combining them.","arXiv :2406 .09024v2 [ astro-ph .IM] 18 Jul 2024  \nE(2)-Equivariant Features in Machine Learning for Morphological Classification of Radio Galaxies  \nNatalie E. P. Lines, 1★ Joan Font-Quer Roset, 1† and Anna M. M. Scaife 1,2  \n1 Jodrell Bank Centre for Astrophysics, Department of Physics & Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL UK  \n2 The Alan Turing Institute, Euston Road, London, NW1 2DB, UK  \nAccepted XXX. Received YYY; in original form ZZZ  \nABSTRACT  \nWith the growth of data from new radio telescope facilities, machine-learning approaches to the morphological classification of radio galaxies are increasingly being utilised. However, while widely employed deep-learning models using convolutional neural networks (CNNs) are equivariant to translations within images, neither CNNs nor most other machine-learning approaches are equivariant to additional isometries of the Euclidean plane, such as rotations and reflections. Recent work has attempted to address this by using 􀀜-steerable CNNs, designed to be equivariant to a specified subset of 2-dimensional Euclidean, E(2), transformations. Although this approach improved model performance, the computational costs were a recognised drawback. Here we consider the use of directly extracted E(2)-equivariant features for the classification of radio galaxies. Specifically, we investigate the use of Minkowski functionals (MFs), Haralick features (HFs) and elliptical Fourier descriptors (EFDs) . We show that, while these features do not perform equivalently well to CNNs in terms of accuracy, they are able to inform the classification of radio galaxies, requiring ∼50 times less computational runtime. We demonstrate that MFs are the most informative, EFDs the least informative, and show that combinations of all three result in only incrementally improved performance, which we suggest is due to information overlap between feature sets.  \nKey words: machine learning – radio continuum: galaxies – techniques: image processing – methods: data analysis  \n1 INTRODUCTION  \nRadio galaxies are galaxies with strong radio emission, typically forming jets and lobes on either side of the host galaxy, which originate from the synchrotron emission of active galactic nuclei (AGNs) . The morphologies of these radio galaxies were first classified into two types by Fanaroff & Riley (1974), known as FR type I (FRI) and type II (FR II) . These two classes are based on the relative locations of highest surface brightness; in FR I, the brightest area lies towards the centre of the AGN, known as edge-darkened, while in FR II the brightest regions lie further away from the centre of the galaxy, known as edge-brightened. These are classified based on their Fanaroff-Riley ratio R FR, defined as the ratio of the distance between the two brightest regions located on opposing sides of the galaxy to the total extension of the galaxy at the lowest threshold. FR I galaxies are those with R FR \u003C 0.5, and FR II are those with R FR > 0.5. In the original investigation by Fanaroff & Riley (1974), these two types were shown to be divided in power: FRI radio galaxies typically have powers at 1 .4 GHz below 􀀥1.4􀀜􀀝 􀁉 = 1025 W Hz−1, while FR II galaxies typically have powers above this. Understanding the formation of these different radio galaxies, the accretion process and interactions of the jets and surrounding environment in the galaxies remains an active area of research, and requires large numbers ofFR type labelled radio galaxies (Hardcastle & Croston 2020) .  \n★ Equal contribution: [natalie.lines@port.ac.uk](natalie.lines@port.ac.uk)  \n† Equal contribution: [joan.fontquer.roset@gmail.com](joan.fontquer.roset@gmail.com)  \nUpcoming telescopes are expected to detect radio galaxies in the millions, with the Square Kilometre Array (SKA) expected to detect upwards of 500 million radio sources (Norris et al. 2015), and the Evolutionary Map of the Universe project (EMU) expected to find 70 million radi","cbCaidYFKE8CyS7r","https://ap.wps.com/l/cbCaidYFKE8CyS7r","pdf",1588361,1,17,"English","en",105,"# Introduction\n## Machine Learning for Radio Galaxy Classification","[{\"question\":\"Why do standard CNNs not fully meet the equivariance needs for radio-galaxy image morphology?\",\"answer\":\"CNNs are translation-equivariant, but they are not generally equivariant to other E(2) isometries such as rotations and reflections, which can change observed orientations in images.\"},{\"question\":\"What E(2)-equivariant features are evaluated for radio galaxy classification?\",\"answer\":\"The document investigates Minkowski functionals (MFs), Haralick features (HFs), and elliptical Fourier descriptors (EFDs) as directly extracted E(2)-equivariant inputs.\"},{\"question\":\"How do the extracted features compare with E(2)-equivariant steerable CNNs in computation and accuracy?\",\"answer\":\"The extracted features do not match CNNs in accuracy, but they enable classification with about 50 times less computational runtime.\"}]","E(2)-Equivariant Features in Machine Learning for Morphological Classification of Radio Galaxies | 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do standard CNNs not fully meet the equivariance needs for radio-galaxy image morphology?","Question",{"text":75,"@type":76},"CNNs are translation-equivariant, but they are not generally equivariant to other E(2) isometries such as rotations and reflections, which can change observed orientations in images.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What E(2)-equivariant features are evaluated for radio galaxy classification?",{"text":80,"@type":76},"The document investigates Minkowski functionals (MFs), Haralick features (HFs), and elliptical Fourier descriptors (EFDs) as directly extracted E(2)-equivariant inputs.",{"name":82,"@type":73,"acceptedAnswer":83},"How do the extracted features compare with E(2)-equivariant steerable CNNs in computation and accuracy?",{"text":84,"@type":76},"The extracted features do not match CNNs in accuracy, but they enable classification with about 50 times less computational 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